MOT for Coordination Compounds | Ligand Field Theory Class 12

MOT for Coordination Compounds

Ligand Field Theory (LFT) | Beyond VBT & CFT

1. Why Molecular Orbital Theory?

While Crystal Field Theory (CFT) is excellent for explaining color and magnetism, it treats metal-ligand bonds as purely ionic (electrostatic). It cannot explain why certain ligands like $CO$ are strong field despite being neutral, nor can it explain the covalent character observed in complexes.

                    Solution: Molecular Orbital Theory (often called Ligand Field Theory in this context) considers the overlap of metal orbitals with Ligand Group Orbitals (LGOs) to form molecular orbitals, accounting for covalency.
                

2. Symmetry Matching & LGOs

In an Octahedral complex ($ML_6$), the metal orbitals are classified by symmetry labels:

$s$ orbital: $a_{1g}$ symmetry.
$p$ orbitals ($p_x, p_y, p_z$): $t_{1u}$ symmetry.
$d$ orbitals ($d_{x^2-y^2}, d_{z^2}$): $e_g$ symmetry.
$d$ orbitals ($d_{xy}, d_{yz}, d_{zx}$): $t_{2g}$ symmetry.

The six ligands form 6 composite $\sigma$-orbitals (LGOs) that match the $a_{1g}, t_{1u}, \text{ and } e_g$ symmetries of the metal.

3. Sigma ($\sigma$) Bonding Diagram

When metal and ligand orbitals overlap:

Bonding MOs: $a_{1g}, t_{1u}, e_g$ (Lower energy, filled by ligand electrons).
Antibonding MOs: $a_{1g}^*, t_{1u}^*, e_g^*$ (Higher energy).
Non-Bonding: The metal $t_{2g}$ orbitals have no matching $\sigma$-symmetry LGOs to interact with. They remain non-bonding (same energy as free metal d-orbitals).

$\Delta_o$ is the energy gap between the Non-bonding $t_{2g}$ and the Antibonding $e_g^*$ orbitals.

4. The Game Changer: $\pi$-Bonding

The most important contribution of MOT is explaining the Spectrochemical Series via $\pi$-interactions. The metal $t_{2g}$ orbitals (non-bonding in $\sigma$-model) can overlap with ligand $\pi$-orbitals.

Case A: $\pi$-Donor Ligands ($F^-, Cl^-, OH^-$)

Ligands have filled p-orbitals.
Ligand $\pi$ orbitals are lower in energy than metal $t_{2g}$.
Result: Metal $t_{2g}$ becomes Antibonding ($\pi^*$) and rises in energy.
Effect: The gap to $e_g^*$ ($\Delta_o$) decreases.
Conclusion: $\pi$-donors are Weak Field Ligands.

Case B: $\pi$-Acceptor Ligands ($CO, CN^-, NO^+$)

Ligands have empty $\pi^*$ orbitals (back-bonding).
Ligand $\pi$ orbitals are higher in energy than metal $t_{2g}$.
Result: Metal $t_{2g}$ becomes Bonding ($\pi$) and lowers in energy.
Effect: The gap to $e_g^*$ ($\Delta_o$) increases significantly.
Conclusion: $\pi$-acceptors are Strong Field Ligands.

5. Explaining the Spectrochemical Series

Based on MOT, ligands are ordered by their ability to split the d-orbitals:

Ligand Type	Interaction	Field Strength ($\Delta_o$)	Examples
$\pi$-Donor	$\sigma$-donor + $\pi$-donor	Small (Weak)	$I^-, Br^-, Cl^-, F^-, OH^-$
$\sigma$-Only	$\sigma$-donor only	Intermediate	$NH_3, H_2O, en$
$\pi$-Acceptor	$\sigma$-donor + $\pi$-acceptor	Large (Strong)	$CN^-, CO, NO^+$

Practice Quiz

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